Not the most elegant, but perhaps fits your needs?
SELECT $table_ranking.*, $table_user.name
FROM $table_ranking INNER JOIN $table_user ON $table_ranking.user_id=$table_user.user_id
WHERE $table_user.user_id IN ($gameIds)
$gameIds should be a CSV list of user IDs put together in your PHP script somewhere (assumption: you're putting a list together in PHP, since this is in the PHP forum...)